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Maximum order of an explicit Runge-Kutta method with n function evaluations in each step.
2

%I #21 Apr 10 2023 10:51:20

%S 1,2,3,4,4,5,6,6,7,7,8

%N Maximum order of an explicit Runge-Kutta method with n function evaluations in each step.

%C a(n) <= n-3 for n >= 10 (Butcher 1985).

%C Observation: first 10 terms coincide with A303735. - _Omar E. Pol_, Oct 04 2018

%C The preceding observation (by Omar E. Pol) holds also for the 11th term. - _Pontus von Brömssen_, Apr 05 2023

%H J. C. Butcher, <a href="https://doi.org/10.1007/BF01935372">The non-existence of ten stage eighth order explicit Runge-Kutta methods</a>, BIT 25 (1985) 521-540.

%H MathOverflow, <a href="https://mathoverflow.net/questions/339041/what-is-the-minimum-number-of-stages-s-required-for-a-runge-kutta-type-numeric">What is the minimum number of stages s required for a Runge-Kutta type numerical method of given order p?</a>, 2019.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">Runge-Kutta methods</a>.

%F a(n) = max{k; A187102(k)<=n}.

%Y Cf. A087803, A187102, A303735.

%K hard,more,nonn

%O 1,2

%A _Pontus von Brömssen_, Mar 04 2011